On the existence of a v232-self map on M(1,4) at the prime 2

M. Behrens; M. Hill; M. J. Hopkins; M. Mahowald

doi:10.4310/HHA.2008.v10.n3.a4

On the existence of a v₂³²-self map on M(1,4) at the prime 2

M. Behrens, M. Hill, M. J. Hopkins, M. Mahowald

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v₁-self map v₁⁴: Σ ⁸M(1) → M(1). Let M(1,4) be the cofiber of this self-map. The purpose of this paper is to prove that M(1,4) admits a minimal v ₂-self map of the form v₂³²: Σ¹⁹²M(1,4) → M(1,4). The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres.

Original language	English (US)
Pages (from-to)	45-84
Number of pages	40
Journal	Homology, Homotopy and Applications
Volume	10
Issue number	3
DOIs	https://doi.org/10.4310/HHA.2008.v10.n3.a4
State	Published - 2008
Externally published	Yes

Keywords

Stable homotopy
V-periodieity

Publisher link

10.4310/HHA.2008.v10.n3.a4

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title = "On the existence of a v232-self map on M(1,4) at the prime 2",

abstract = "Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v1-self map v14: Σ 8M(1) → M(1). Let M(1,4) be the cofiber of this self-map. The purpose of this paper is to prove that M(1,4) admits a minimal v 2-self map of the form v232: Σ192M(1,4) → M(1,4). The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres.",

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T1 - On the existence of a v232-self map on M(1,4) at the prime 2

AU - Behrens, M.

AU - Hill, M.

AU - Hopkins, M. J.

AU - Mahowald, M.

PY - 2008

Y1 - 2008

N2 - Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v1-self map v14: Σ 8M(1) → M(1). Let M(1,4) be the cofiber of this self-map. The purpose of this paper is to prove that M(1,4) admits a minimal v 2-self map of the form v232: Σ192M(1,4) → M(1,4). The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres.

AB - Let M(1) be the mod 2 Moore spectrum. J.F. Adams proved that M(1) admits a minimal v1-self map v14: Σ 8M(1) → M(1). Let M(1,4) be the cofiber of this self-map. The purpose of this paper is to prove that M(1,4) admits a minimal v 2-self map of the form v232: Σ192M(1,4) → M(1,4). The existence of this map implies the existence of many 192-periodic families of elements in the stable homotopy groups of spheres.

KW - Stable homotopy

KW - V-periodieity

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